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MOLLER Bayesian Code
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import sys
sys.path.append('/home/elhamm/projects/def-wdconinc/elhamm/my_venv/lib/python3.11/site-packages')
import math
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import beta
from numpy import random
from scipy.stats import norm
import nest_asyncio
import arviz as az
from numpy.core.shape_base import vstack
import pystan
#**************************************************************************************************************************************************
sns.set_style("whitegrid") # Set the style directly using seaborn
#sns.set(font="Times New Roman") # Set the font using seaborn
plt.rc('axes', labelsize=16)
plt.rc('axes', titlesize=16)
plt.rc('figure', titlesize=20)
#**************************************************************************************************************************************************
seeds = np.random.seed(401)
pi = math.pi
ActualRunTime = 8256 #Hours
Runtime = int(ActualRunTime) #Hours
N_L = (int(0.9 * Runtime)) #Hours
N_T = (int(0.1 * Runtime)) #Hours
Window_L = ((0.9*Runtime)/(N_L))
Window_T = ((0.1*Runtime)/(N_T))
num_PionDet = 28
num_MainDet = 84
Theta_uncertainty = 0.017453292519943295 #1degree
Phi_uncertainty = 0.017453292519943295 #1degree
print("N_L =", N_L, "N_T =", N_T, "Window_L=", Window_L, "Window_T=", Window_T)
#**************************************************************************************************************************************************
#Rates values from simulations at
#/home/elhamm/projects/def-wdconinc/elhamm/PionDetectorOptimization/simulation/run/remoll-Updated-July2023/Moller_Asymmetry/MainDet
#/home/elhamm/projects/def-wdconinc/elhamm/PionDetectorOptimization/simulation/run/remoll-Updated-July2023/Pion_Asymmetry/PionDet
I= 65 # Current (Micro-A [GHz])
Rate_Mollers_PionDet = 4.0362586*1e9
Rate_Pions_PionDet = 0.98928794*1e9
Rates_PionDet = Rate_Pions_PionDet + Rate_Mollers_PionDet
Total_Rates_PionDet = (Rates_PionDet/(50*28*85))*65
Uncertainty_L_PionDet = ((1/np.sqrt(Total_Rates_PionDet*Window_L*3600))*1e9)*(91/82)
Uncertainty_T_PionDet = ((1/np.sqrt(Total_Rates_PionDet*Window_T*3600))*1e9)*(91/82)
Rate_Mollers_MainDet = 7.1074070e+12
Rate_Pions_MainDet =7.6445978*1e9
Rates_MainDet = Rate_Pions_MainDet + Rate_Mollers_MainDet
Total_Rates_MainDet = (Rates_MainDet/(50*84))
Uncertainty_L_MainDet = ((1/np.sqrt(Total_Rates_MainDet*Window_L*3600))*1e9)*(91/82)
Uncertainty_T_MainDet = ((1/np.sqrt(Total_Rates_MainDet*Window_T*3600))*1e9)*(91/82)
print("Total_Rates_PionDet=", Total_Rates_PionDet, "Total_Rates_MainDet=", Total_Rates_MainDet, "Uncertainty_L_PionDet=", Uncertainty_L_PionDet, "Uncertainty_L_MainDet=", Uncertainty_L_MainDet, "Uncertainty_T_PionDet=", Uncertainty_T_PionDet, "Uncertainty_T_MainDet=", Uncertainty_T_MainDet)
#**************************************************************************************************************************************************
Pion_Asy_L_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Pion_Asymmetry_Longitudinal_PionDet.csv')
Pion_Asy_TV_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Pion_Asymmetry_Transverse_Vertical_PionDet.csv')
Pion_Asy_TH_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Pion_Asymmetry_Transverse_Horizontal_PionDet.csv')
Pion_Asy_L_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Pion_Asymmetry-longitudinal-MainDet-Ring5.csv')
Pion_Asy_TV_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Pion_Asymmetry-transverse-vertical-MainDet-Ring5.csv')
Pion_Asy_TH_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Pion_Asymmetry-transverse-horizontal-MainDet-Ring5.csv')
Moller_Asy_L_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Moller_Asymmetry_Longitudinal_PionDet.csv')
Moller_Asy_TV_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Moller_Asymmetry-transverse-vertical-PionDet.csv')
Moller_Asy_TH_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Moller_Asymmetry-transverse-horizontal-PionDet.csv')
Moller_Asy_L_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Moller_Asymmetry-longitudinal-MainDet-Ring5.csv')
Moller_Asy_TV_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Moller_Asymmetry-transverse-vertical-MainDet-Ring5.csv')
Moller_Asy_TH_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Moller_Asymmetry-transverse-horizontal-MainDet-Ring5.csv')
Dilution_Factor_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Dilution Factor_PionDet.csv')
Dilution_Factor_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Dilution Factor_MainDet.csv')
Normalized_Pion_Asy_L_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Pion_Asymmetry_Longitudinal_PionDet.csv')
Normalized_Pion_Asy_L_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Pion_Asymmetry-longitudinal-MainDet-Ring5.csv')
Normalized_Moller_Asy_L_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Moller_Asymmetry_Longitudinal_PionDet.csv')
Normalized_Moller_Asy_L_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Moller_Asymmetry-longitudinal-MainDet-Ring5.csv')
Normalized_Moller_Asy_TV_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Moller_Asymmetry-transverse-vertical-PionDet.csv')
Normalized_Moller_Asy_TH_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Moller_Asymmetry-transverse-horizontal-PionDet.csv')
Normalized_Pion_Asy_TV_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Pion_Asymmetry_Transverse_Vertical_PionDet.csv')
Normalized_Pion_Asy_TH_PionDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Pion_Asymmetry_Transverse_Horizontal_PionDet.csv')
Normalized_Moller_Asy_TV_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Moller_Asymmetry-transverse-vertical-MainDet-Ring5.csv')
Normalized_Moller_Asy_TH_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Moller_Asymmetry-transverse-horizontal-MainDet-Ring5.csv')
Normalized_Pion_Asy_TV_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Pion_Asymmetry-transverse-vertical-MainDet-Ring5.csv')
Normalized_Pion_Asy_TH_MainDet = pd.read_csv('/lustre06/project/6041615/elhamm/AsymmetryExtraction/Moller/Normalized_Pion_Asymmetry-transverse-horizontal-MainDet-Ring5.csv')
# Convert columns to numpy arrays
Data_A_eL_PionDet = Normalized_Moller_Asy_L_PionDet.Normalized_Moller_Asymmetry
Data_A_eT_V_PionDet = Normalized_Moller_Asy_TV_PionDet.Normalized_Moller_Asymmetry
Data_A_eT_H_PionDet = Normalized_Moller_Asy_TH_PionDet.Normalized_Moller_Asymmetry
Data_A_piL_PionDet = Normalized_Pion_Asy_L_PionDet.Normalized_Pion_Asymmetry
Data_A_piT_V_PionDet = Normalized_Pion_Asy_TV_PionDet.Normalized_Pion_Asymmetry
Data_A_piT_H_PionDet = Normalized_Pion_Asy_TH_PionDet.Normalized_Pion_Asymmetry
Data_A_eL_MainDet = Normalized_Moller_Asy_L_MainDet.Normalized_Moller_Asymmetry
Data_A_eT_V_MainDet = Normalized_Moller_Asy_TV_MainDet.Normalized_Moller_Asymmetry
Data_A_eT_H_MainDet = Normalized_Moller_Asy_TH_MainDet.Normalized_Moller_Asymmetry
Data_A_piL_MainDet = Normalized_Pion_Asy_L_MainDet.Normalized_Pion_Asymmetry
Data_A_piT_V_MainDet = Normalized_Pion_Asy_TV_MainDet.Normalized_Pion_Asymmetry
Data_A_piT_H_MainDet = Normalized_Pion_Asy_TH_MainDet.Normalized_Pion_Asymmetry
#**************************************************************************************************************************************************
#Generating Mock Data - Longitudinal
Measured_Asymmetry_PionDet_L = np.zeros((num_PionDet, N_L))
Measured_Asymmetry_MainDet_L = np.zeros((num_MainDet, N_L))
Measured_Asymmetry_PionDet_L_True = np.zeros((num_PionDet, N_L))
Measured_Asymmetry_MainDet_L_True = np.zeros((num_MainDet, N_L))
partial_f_Pi_PionDet_L_True = np.zeros((num_PionDet, N_L))
partial_theta_L_PionDet_True = np.zeros((num_PionDet, N_L))
partial_phi_L_PionDet_True = np.zeros((num_PionDet, N_L))
dMeasured_Asymmetry_PionDet_L_True = np.zeros((num_PionDet, N_L))
#Choose one theta and phi for the whole run
theta_L = np.random.normal(0, Theta_uncertainty)
phi_L = np.random.normal(0, pi)
for iteration in range(N_L):
Pion_Asymmetry_L_PionDet = []
Moller_Asymmetry_L_PionDet = []
dAsymmetry_L_PionDet = []
Pion_Asymmetry_TV_PionDet = []
Pion_Asymmetry_TH_PionDet =[]
Moller_Asymmetry_TV_PionDet = []
Moller_Asymmetry_TH_PionDet =[]
f_Pi_PionDet = []
df_Pi_PionDet = []
Pion_Asymmetry_L_MainDet = []
Moller_Asymmetry_L_MainDet = []
dAsymmetry_L_MainDet = []
Pion_Asymmetry_TV_MainDet = []
Pion_Asymmetry_TH_MainDet =[]
Moller_Asymmetry_TV_MainDet = []
Moller_Asymmetry_TH_MainDet =[]
f_Pi_MainDet = []
df_Pi_MainDet = []
for i in range(num_PionDet):
Pion_Asymmetry_L_PionDet_value = (Pion_Asy_L_PionDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_L_PionDet.append(Pion_Asymmetry_L_PionDet_value)
Moller_Asymmetry_L_PionDet_value = (Moller_Asy_L_PionDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_L_PionDet.append(Moller_Asymmetry_L_PionDet_value)
Pion_Asymmetry_TV_PionDet_value = (Pion_Asy_TV_PionDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_TV_PionDet.append(Pion_Asymmetry_TV_PionDet_value)
Pion_Asymmetry_TH_PionDet_value = (Pion_Asy_TH_PionDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_TH_PionDet.append(Pion_Asymmetry_TH_PionDet_value)
Moller_Asymmetry_TV_PionDet_value = (Moller_Asy_TV_PionDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_TV_PionDet.append(Moller_Asymmetry_TV_PionDet_value)
Moller_Asymmetry_TH_PionDet_value = (Moller_Asy_TH_PionDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_TH_PionDet.append(Moller_Asymmetry_TH_PionDet_value)
f_Pi_PionDet_value = (Dilution_Factor_PionDet.at[i, 'Ratio'])
f_Pi_PionDet.append(f_Pi_PionDet_value)
df_Pi_PionDet_value = (Dilution_Factor_PionDet.at[i, 'Ratio_Uncertainty'])
df_Pi_PionDet.append(df_Pi_PionDet_value)
# Convert the entire list to a numpy array
A_piL_PionDet = np.array(Pion_Asymmetry_L_PionDet)
A_eL_PionDet = np.array(Moller_Asymmetry_L_PionDet)
A_piTV_PionDet = np.array(Pion_Asymmetry_TV_PionDet)
A_eTV_PionDet = np.array(Moller_Asymmetry_TV_PionDet)
A_piTH_PionDet = np.array(Pion_Asymmetry_TH_PionDet)
A_eTH_PionDet = np.array(Moller_Asymmetry_TH_PionDet)
f_Pi_PionDet = np.array(f_Pi_PionDet)
for i in range(num_PionDet):
Measured_Asymmetry_PionDet_L_value = (1 - f_Pi_PionDet[i]) * (A_eL_PionDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_eTV_PionDet[i]*np.sin(phi_L) + A_eTH_PionDet[i]*np.cos(phi_L))) + f_Pi_PionDet[i] * (A_piL_PionDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_piTV_PionDet[i]*np.sin(phi_L) + A_piTH_PionDet[i]*np.cos(phi_L)))
Measured_Asymmetry_PionDet_L[i, iteration] = np.random.normal(Measured_Asymmetry_PionDet_L_value, Uncertainty_L_PionDet)
Measured_Asymmetry_PionDet_L_value_True = (1 - f_Pi_PionDet[i]) * (A_eL_PionDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_eTV_PionDet[i]*np.sin(phi_L) + A_eTH_PionDet[i]*np.cos(phi_L))) + f_Pi_PionDet[i] * (A_piL_PionDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_piTV_PionDet[i]*np.sin(phi_L) + A_piTH_PionDet[i]*np.cos(phi_L)))
Measured_Asymmetry_PionDet_L_True[i, iteration] = Measured_Asymmetry_PionDet_L_value_True
partial_f_Pi = -(A_eL_PionDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_eTV_PionDet[i]*np.sin(phi_L) + A_eTH_PionDet[i]*np.cos(phi_L))) + (A_piL_PionDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_piTV_PionDet[i]*np.sin(phi_L) + A_piTH_PionDet[i]*np.cos(phi_L)))
partial_theta = (1 - f_Pi_PionDet[i]) * (A_eL_PionDet[i] * (-np.sin(theta_L)) + np.cos(theta_L) * (A_eTV_PionDet[i]*np.sin(phi_L) + A_eTH_PionDet[i]*np.cos(phi_L))) + f_Pi_PionDet[i] * (A_piL_PionDet[i] * (-np.sin(theta_L)) + np.cos(theta_L) * (A_piTV_PionDet[i]*np.sin(phi_L) + A_piTH_PionDet[i]*np.cos(phi_L)))
partial_phi = (1 - f_Pi_PionDet[i]) * (A_eL_PionDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_eTV_PionDet[i]*np.cos(phi_L) + A_eTH_PionDet[i]*(-np.sin(phi_L)))) + f_Pi_PionDet[i] * (A_piL_PionDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_piTV_PionDet[i]*np.cos(phi_L) + A_piTH_PionDet[i]*(-np.sin(phi_L))))
# Store the computed partial derivatives
partial_f_Pi_PionDet_L_True[i, iteration] = partial_f_Pi
partial_theta_L_PionDet_True[i, iteration] = partial_theta
partial_phi_L_PionDet_True[i, iteration] = partial_phi
#dMeasured_Asymmetry_PionDet_L_True[i] = np.sqrt((partial_f_Pi_PionDet_L_True[i]*df_Pi_PionDet_L[i])**2 + (partial_theta_L_PionDet_True[i]*dtheta_L_PionDet[i])**2 + (partial_phi_L_PionDet_True[i]*dphi_L_PionDet[i,j])**2)
for i in range(num_MainDet):
Pion_Asymmetry_L_MainDet_value = (Pion_Asy_L_MainDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_L_MainDet.append(Pion_Asymmetry_L_MainDet_value)
Moller_Asymmetry_L_MainDet_value = (Moller_Asy_L_MainDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_L_MainDet.append(Moller_Asymmetry_L_MainDet_value)
Pion_Asymmetry_TV_MainDet_value = (Pion_Asy_TV_MainDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_TV_MainDet.append(Pion_Asymmetry_TV_MainDet_value)
Pion_Asymmetry_TH_MainDet_value = (Pion_Asy_TH_MainDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_TH_MainDet.append(Pion_Asymmetry_TH_MainDet_value)
Moller_Asymmetry_TV_MainDet_value = (Moller_Asy_TV_MainDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_TV_MainDet.append(Moller_Asymmetry_TV_MainDet_value)
Moller_Asymmetry_TH_MainDet_value = (Moller_Asy_TH_MainDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_TH_MainDet.append(Moller_Asymmetry_TH_MainDet_value)
f_Pi_MainDet_value = (Dilution_Factor_MainDet.at[i, 'Ratio'])
f_Pi_MainDet.append(f_Pi_MainDet_value)
df_Pi_MainDet_value = (Dilution_Factor_MainDet.at[i, 'Ratio_Uncertainty'])
df_Pi_MainDet.append(df_Pi_MainDet_value)
# Convert the entire list to a numpy array
A_piL_MainDet = np.array(Pion_Asymmetry_L_MainDet)
A_eL_MainDet = np.array(Moller_Asymmetry_L_MainDet)
A_piTV_MainDet = np.array(Pion_Asymmetry_TV_MainDet)
A_eTV_MainDet = np.array(Moller_Asymmetry_TV_MainDet)
A_piTH_MainDet = np.array(Pion_Asymmetry_TH_MainDet)
A_eTH_MainDet = np.array(Moller_Asymmetry_TH_MainDet)
f_Pi_MainDet = np.array(f_Pi_MainDet)
for i in range(num_MainDet):
Measured_Asymmetry_MainDet_L_value = (1 - f_Pi_MainDet[i]) * (A_eL_MainDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_eTV_MainDet[i]*np.sin(phi_L) + A_eTH_MainDet[i]*np.cos(phi_L))) + f_Pi_MainDet[i] * (A_piL_MainDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_piTV_MainDet[i]*np.sin(phi_L) + A_piTH_MainDet[i]*np.cos(phi_L)))
Measured_Asymmetry_MainDet_L[i, iteration] = np.random.normal(Measured_Asymmetry_MainDet_L_value, Uncertainty_L_MainDet)
Measured_Asymmetry_MainDet_L_value_True = (1 - f_Pi_MainDet[i]) * (A_eL_MainDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_eTV_MainDet[i]*np.sin(phi_L) + A_eTH_MainDet[i]*np.cos(phi_L))) + f_Pi_MainDet[i] * (A_piL_MainDet[i] * np.cos(theta_L) + np.sin(theta_L) * (A_piTV_MainDet[i]*np.sin(phi_L) + A_piTH_MainDet[i]*np.cos(phi_L)))
Measured_Asymmetry_MainDet_L_True[i, iteration] = Measured_Asymmetry_MainDet_L_value_True
print("Measured_Asymmetry_PionDet_L.shape:", Measured_Asymmetry_PionDet_L.shape)
print("Measured_Asymmetry_PionDet_L_True.shape:", Measured_Asymmetry_PionDet_L_True.shape)
print("Measured_Asymmetry_MainDet_L.shape:", Measured_Asymmetry_MainDet_L.shape)
print("Measured_Asymmetry_MainDet_L_True.shape:", Measured_Asymmetry_MainDet_L_True.shape)
print("theta_L:", theta_L)
print("phi_L:", phi_L)
#**************************************************************************************************************************************************
#Generating Mock Data - Transverse
Measured_Asymmetry_PionDet_T = np.zeros((num_PionDet, N_T))
Measured_Asymmetry_MainDet_T = np.zeros((num_MainDet, N_T))
Measured_Asymmetry_PionDet_T_True = np.zeros((num_PionDet, N_T))
Measured_Asymmetry_MainDet_T_True = np.zeros((num_MainDet, N_T))
#Choose one theta and phi for the whole run
theta_T = np.random.normal(pi/2, Theta_uncertainty)
phi_T = np.random.normal(0, Phi_uncertainty)
for iteration in range(N_T):
Pion_Asymmetry_L_PionDet = []
Moller_Asymmetry_L_PionDet = []
dAsymmetry_L_PionDet = []
Pion_Asymmetry_TV_PionDet = []
Pion_Asymmetry_TH_PionDet =[]
Moller_Asymmetry_TV_PionDet = []
Moller_Asymmetry_TH_PionDet =[]
f_Pi_PionDet = []
df_Pi_PionDet = []
Pion_Asymmetry_L_MainDet = []
Moller_Asymmetry_L_MainDet = []
dAsymmetry_L_MainDet = []
Pion_Asymmetry_TV_MainDet = []
Pion_Asymmetry_TH_MainDet =[]
Moller_Asymmetry_TV_MainDet = []
Moller_Asymmetry_TH_MainDet =[]
f_Pi_MainDet = []
df_Pi_MainDet = []
for i in range(num_PionDet):
Pion_Asymmetry_L_PionDet_value = (Pion_Asy_L_PionDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_L_PionDet.append(Pion_Asymmetry_L_PionDet_value)
Moller_Asymmetry_L_PionDet_value = (Moller_Asy_L_PionDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_L_PionDet.append(Moller_Asymmetry_L_PionDet_value)
Pion_Asymmetry_TV_PionDet_value = (Pion_Asy_TV_PionDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_TV_PionDet.append(Pion_Asymmetry_TV_PionDet_value)
Pion_Asymmetry_TH_PionDet_value = (Pion_Asy_TH_PionDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_TH_PionDet.append(Pion_Asymmetry_TH_PionDet_value)
Moller_Asymmetry_TV_PionDet_value = (Moller_Asy_TV_PionDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_TV_PionDet.append(Moller_Asymmetry_TV_PionDet_value)
Moller_Asymmetry_TH_PionDet_value = (Moller_Asy_TH_PionDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_TH_PionDet.append(Moller_Asymmetry_TH_PionDet_value)
f_Pi_PionDet_value = (Dilution_Factor_PionDet.at[i, 'Ratio'])
f_Pi_PionDet.append(f_Pi_PionDet_value)
df_Pi_PionDet_value = (Dilution_Factor_PionDet.at[i, 'Ratio_Uncertainty'])
df_Pi_PionDet.append(df_Pi_PionDet_value)
# Convert the entire list to a numpy array
A_piL_PionDet = np.array(Pion_Asymmetry_L_PionDet)
A_eL_PionDet = np.array(Moller_Asymmetry_L_PionDet)
A_piTV_PionDet = np.array(Pion_Asymmetry_TV_PionDet)
A_eTV_PionDet = np.array(Moller_Asymmetry_TV_PionDet)
A_piTH_PionDet = np.array(Pion_Asymmetry_TH_PionDet)
A_eTH_PionDet = np.array(Moller_Asymmetry_TH_PionDet)
f_Pi_PionDet = np.array(f_Pi_PionDet)
for i in range(num_PionDet):
Measured_Asymmetry_PionDet_T_value = (1 - f_Pi_PionDet[i]) * (A_eL_PionDet[i] * np.cos(theta_T) + np.sin(theta_T) * (A_eTV_PionDet[i]*np.sin(phi_T) + A_eTH_PionDet[i]*np.cos(phi_T))) + f_Pi_PionDet[i] * (A_piL_PionDet[i] * np.cos(theta_T) + np.sin(theta_T) * (A_piTV_PionDet[i]*np.sin(phi_T) + A_piTH_PionDet[i]*np.cos(phi_T)))
Measured_Asymmetry_PionDet_T[i, iteration] = np.random.normal(Measured_Asymmetry_PionDet_T_value, Uncertainty_T_PionDet)
Measured_Asymmetry_PionDet_T_value_True = (1 - f_Pi_PionDet[i]) * (A_eL_PionDet[i] * np.cos(theta_T) + np.sin(theta_T) * (A_eTV_PionDet[i]*np.sin(phi_T) + A_eTH_PionDet[i]*np.cos(phi_T))) + f_Pi_PionDet[i] * (A_piL_PionDet[i] * np.cos(theta_T) + np.sin(theta_T) * (A_piTV_PionDet[i]*np.sin(phi_T) + A_piTH_PionDet[i]*np.cos(phi_T)))
Measured_Asymmetry_PionDet_T_True[i, iteration] = Measured_Asymmetry_PionDet_T_value_True
for i in range(num_MainDet):
Pion_Asymmetry_L_MainDet_value = (Pion_Asy_L_MainDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_L_MainDet.append(Pion_Asymmetry_L_MainDet_value)
Moller_Asymmetry_L_MainDet_value = (Moller_Asy_L_MainDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_L_MainDet.append(Moller_Asymmetry_L_MainDet_value)
Pion_Asymmetry_TV_MainDet_value = (Pion_Asy_TV_MainDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_TV_MainDet.append(Pion_Asymmetry_TV_MainDet_value)
Pion_Asymmetry_TH_MainDet_value = (Pion_Asy_TH_MainDet.at[i, 'Pion_Asymmetry'])
Pion_Asymmetry_TH_MainDet.append(Pion_Asymmetry_TH_MainDet_value)
Moller_Asymmetry_TV_MainDet_value = (Moller_Asy_TV_MainDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_TV_MainDet.append(Moller_Asymmetry_TV_MainDet_value)
Moller_Asymmetry_TH_MainDet_value = (Moller_Asy_TH_MainDet.at[i, 'Moller_Asymmetry'])
Moller_Asymmetry_TH_MainDet.append(Moller_Asymmetry_TH_MainDet_value)
f_Pi_MainDet_value = (Dilution_Factor_MainDet.at[i, 'Ratio'])
f_Pi_MainDet.append(f_Pi_MainDet_value)
# Convert the entire list to a numpy array
A_piL_MainDet = np.array(Pion_Asymmetry_L_MainDet)
A_eL_MainDet = np.array(Moller_Asymmetry_L_MainDet)
A_piTV_MainDet = np.array(Pion_Asymmetry_TV_MainDet)
A_eTV_MainDet = np.array(Moller_Asymmetry_TV_MainDet)
A_piTH_MainDet = np.array(Pion_Asymmetry_TH_MainDet)
A_eTH_MainDet = np.array(Moller_Asymmetry_TH_MainDet)
f_Pi_MainDet = np.array(f_Pi_MainDet)
for i in range(num_MainDet):
Measured_Asymmetry_MainDet_T_value = (1 - f_Pi_MainDet[i]) * (A_eL_MainDet[i] * np.cos(theta_T) + np.sin(theta_T) * (A_eTV_MainDet[i]*np.sin(phi_T) + A_eTH_MainDet[i]*np.cos(phi_T))) + f_Pi_MainDet[i] * (A_piL_MainDet[i] * np.cos(theta_T) + np.sin(theta_T) * (A_piTV_MainDet[i]*np.sin(phi_T) + A_piTH_MainDet[i]*np.cos(phi_T)))
Measured_Asymmetry_MainDet_T[i, iteration] = np.random.normal(Measured_Asymmetry_MainDet_T_value, Uncertainty_T_MainDet)
Measured_Asymmetry_MainDet_T_value_True = (1 - f_Pi_MainDet[i]) * (A_eL_MainDet[i] * np.cos(theta_T) + np.sin(theta_T) * (A_eTV_MainDet[i]*np.sin(phi_T) + A_eTH_MainDet[i]*np.cos(phi_T))) + f_Pi_MainDet[i] * (A_piL_MainDet[i] * np.cos(theta_T) + np.sin(theta_T) * (A_piTV_MainDet[i]*np.sin(phi_T) + A_piTH_MainDet[i]*np.cos(phi_T)))
Measured_Asymmetry_MainDet_T_True[i, iteration] = Measured_Asymmetry_MainDet_T_value_True
print("Measured_Asymmetry_PionDet_T.shape:", Measured_Asymmetry_PionDet_T.shape)
print("Measured_Asymmetry_PionDet_T_True.shape:", Measured_Asymmetry_PionDet_T_True.shape)
print("Measured_Asymmetry_MainDet_T.shape:", Measured_Asymmetry_MainDet_T.shape)
print("Measured_Asymmetry_MainDet_T_True.shape:", Measured_Asymmetry_MainDet_T_True.shape)
print("theta_T:", theta_T)
print("phi_T:", phi_T)
#**************************************************************************************************************************************************
dMeasured_Asymmetry_PionDet_L = []
dMeasured_Asymmetry_PionDet_T = []
dMeasured_Asymmetry_MainDet_L = []
dMeasured_Asymmetry_MainDet_T = []
for i in range(28):
dMeasured_Asymmetry_PionDet_L.append(np.array([Uncertainty_L_PionDet]*N_L))
dMeasured_Asymmetry_PionDet_T.append(np.array([Uncertainty_T_PionDet]*N_T))
for i in range(84):
dMeasured_Asymmetry_MainDet_L.append(np.array([Uncertainty_L_MainDet]*N_L))
dMeasured_Asymmetry_MainDet_T.append(np.array([Uncertainty_T_MainDet]*N_T))
print("np.shape(dMeasured_Asymmetry_PionDet_L):", np.shape(dMeasured_Asymmetry_PionDet_L))
print("np.shape(dMeasured_Asymmetry_MainDet_L):", np.shape(dMeasured_Asymmetry_MainDet_L))
print("np.shape(dMeasured_Asymmetry_PionDet_T):", np.shape(dMeasured_Asymmetry_PionDet_T))
print("np.shape(dMeasured_Asymmetry_MainDet_T):", np.shape(dMeasured_Asymmetry_MainDet_T))
#**************************************************************************************************************************************************
f_Pi_PionDet_L = []
f_Pi_MainDet_L = []
df_Pi_PionDet_L = []
df_Pi_MainDet_L = []
f_Pi_PionDet_T = []
f_Pi_MainDet_T = []
df_Pi_PionDet_T = []
df_Pi_MainDet_T = []
for i in range(28):
f_Pi_PionDet_L_value = (Dilution_Factor_PionDet.at[i, 'Ratio'])
f_Pi_PionDet_L.append(np.array([f_Pi_PionDet_L_value]*N_L))
df_Pi_PionDet_L_value = (Dilution_Factor_PionDet.at[i, 'Ratio_Uncertainty'])
df_Pi_PionDet_L.append(np.array([df_Pi_PionDet_L_value]*N_L))
f_Pi_PionDet_T_value = (Dilution_Factor_PionDet.at[i, 'Ratio'])
f_Pi_PionDet_T.append(np.array([f_Pi_PionDet_T_value]*N_T))
df_Pi_PionDet_T_value = (Dilution_Factor_PionDet.at[i, 'Ratio_Uncertainty'])
df_Pi_PionDet_T.append(np.array([df_Pi_PionDet_T_value]*N_T))
for i in range(84):
f_Pi_MainDet_L_value = (Dilution_Factor_MainDet.at[i, 'Ratio'])
f_Pi_MainDet_L.append(np.array([f_Pi_MainDet_L_value]*N_L))
df_Pi_MainDet_L_value = (Dilution_Factor_MainDet.at[i, 'Ratio_Uncertainty'])
df_Pi_MainDet_L.append(np.array([df_Pi_MainDet_L_value]*N_L))
f_Pi_MainDet_T_value = (Dilution_Factor_MainDet.at[i, 'Ratio'])
f_Pi_MainDet_T.append(np.array([f_Pi_MainDet_T_value]*N_T))
df_Pi_MainDet_T_value = (Dilution_Factor_MainDet.at[i, 'Ratio_Uncertainty'])
df_Pi_MainDet_T.append(np.array([df_Pi_MainDet_T_value]*N_T))
f_Pi_PionDet_L = np.array(f_Pi_PionDet_L)
f_Pi_PionDet_T = np.array(f_Pi_PionDet_T)
f_Pi_MainDet_L = np.array(f_Pi_MainDet_L)
f_Pi_MainDet_T = np.array(f_Pi_MainDet_T)
df_Pi_PionDet_L = np.array(df_Pi_PionDet_L)
df_Pi_PionDet_T = np.array(df_Pi_PionDet_T)
df_Pi_MainDet_L = np.array(df_Pi_MainDet_L)
df_Pi_MainDet_T = np.array(df_Pi_MainDet_T)
print("f_Pi_PionDet_L.shape:", f_Pi_PionDet_L.shape)
print("f_Pi_PionDet_T.shape:", f_Pi_PionDet_T.shape)
print("f_Pi_MainDet_L.shape:", f_Pi_MainDet_L.shape)
print("f_Pi_MainDet_T.shape:", f_Pi_MainDet_T.shape)
print("df_Pi_PionDet_L.shape:", df_Pi_PionDet_L.shape)
print("df_Pi_PionDet_T.shape:", df_Pi_PionDet_T.shape)
print("df_Pi_MainDet_L.shape:", df_Pi_MainDet_L.shape)
print("df_Pi_MainDet_T.shape:", df_Pi_MainDet_T.shape)
#**************************************************************************************************************************************************
A_eL_L_PionDet = [None]*28
A_eT_V_L_PionDet = [None]*28
A_eT_H_L_PionDet = [None]*28
A_piL_L_PionDet = [None]*28
A_piT_V_L_PionDet = [None]*28
A_piT_H_L_PionDet = [None]*28
A_eL_L_MainDet = [None]*84
A_eT_V_L_MainDet = [None]*84
A_eT_H_L_MainDet = [None]*84
A_piL_L_MainDet = [None]*84
A_piT_V_L_MainDet = [None]*84
A_piT_H_L_MainDet = [None]*84
A_eL_T_PionDet = [None]*28
A_eT_V_T_PionDet = [None]*28
A_eT_H_T_PionDet = [None]*28
A_piL_T_PionDet = [None]*28
A_piT_V_T_PionDet = [None]*28
A_piT_H_T_PionDet = [None]*28
A_eL_T_MainDet = [None]*84
A_eT_V_T_MainDet = [None]*84
A_eT_H_T_MainDet = [None]*84
A_piL_T_MainDet = [None]*84
A_piT_V_T_MainDet = [None]*84
A_piT_H_T_MainDet = [None]*84
for i in range(0, 28):
A_eL_L_PionDet[i] = np.array([Data_A_eL_PionDet[i]]*N_L)
A_eT_V_L_PionDet[i] = np.array([Data_A_eT_V_PionDet[i]]*N_L)
A_eT_H_L_PionDet[i] = np.array([Data_A_eT_H_PionDet[i]]*N_L)
A_piL_L_PionDet[i] = np.array([Data_A_piL_PionDet[i]]*N_L)
A_piT_V_L_PionDet[i] = np.array([Data_A_piT_V_PionDet[i]]*N_L)
A_piT_H_L_PionDet[i] = np.array([Data_A_piT_H_PionDet[i]]*N_L)
A_eL_T_PionDet[i] = np.array([Data_A_eL_PionDet[i]]*N_T)
A_eT_V_T_PionDet[i] = np.array([Data_A_eT_V_PionDet[i]]*N_T)
A_eT_H_T_PionDet[i] = np.array([Data_A_eT_H_PionDet[i]]*N_T)
A_piL_T_PionDet[i] = np.array([Data_A_piL_PionDet[i]]*N_T)
A_piT_V_T_PionDet[i] = np.array([Data_A_piT_V_PionDet[i]]*N_T)
A_piT_H_T_PionDet[i] = np.array([Data_A_piT_H_PionDet[i]]*N_T)
for i in range(0, 84):
A_eL_L_MainDet[i] = np.array([Data_A_eL_MainDet[i]]*N_L)
A_eT_V_L_MainDet[i] = np.array([Data_A_eT_V_MainDet[i]]*N_L)
A_eT_H_L_MainDet[i] = np.array([Data_A_eT_H_MainDet[i]]*N_L)
A_piL_L_MainDet[i] = np.array([Data_A_piL_MainDet[i]]*N_L)
A_piT_V_L_MainDet[i] = np.array([Data_A_piT_V_MainDet[i]]*N_L)
A_piT_H_L_MainDet[i] = np.array([Data_A_piT_H_MainDet[i]]*N_L)
A_eL_T_MainDet[i] = np.array([Data_A_eL_MainDet[i]]*N_T)
A_eT_V_T_MainDet[i] = np.array([Data_A_eT_V_MainDet[i]]*N_T)
A_eT_H_T_MainDet[i] = np.array([Data_A_eT_H_MainDet[i]]*N_T)
A_piL_T_MainDet[i] = np.array([Data_A_piL_MainDet[i]]*N_T)
A_piT_V_T_MainDet[i] = np.array([Data_A_piT_V_MainDet[i]]*N_T)
A_piT_H_T_MainDet[i] = np.array([Data_A_piT_H_MainDet[i]]*N_T)
A_eL_L_PionDet = np.array(A_eL_L_PionDet)
A_eT_V_L_PionDet = np.array(A_eT_V_L_PionDet)
A_eT_H_L_PionDet = np.array(A_eT_H_L_PionDet)
A_piL_L_PionDet = np.array(A_piL_L_PionDet)
A_piT_V_L_PionDet = np.array(A_piT_V_L_PionDet)
A_piT_H_L_PionDet = np.array(A_piT_H_L_PionDet)
A_eL_T_PionDet = np.array(A_eL_T_PionDet)
A_eT_V_T_PionDet = np.array(A_eT_V_T_PionDet)
A_eT_H_T_PionDet = np.array(A_eT_H_T_PionDet)
A_piL_T_PionDet = np.array(A_piL_T_PionDet)
A_piT_V_T_PionDet = np.array(A_piT_V_T_PionDet)
A_piT_H_T_PionDet = np.array(A_piT_H_T_PionDet)
A_eL_L_MainDet = np.array(A_eL_L_MainDet)
A_eT_V_L_MainDet = np.array(A_eT_V_L_MainDet)
A_eT_H_L_MainDet = np.array(A_eT_H_L_MainDet)
A_piL_L_MainDet = np.array(A_piL_L_MainDet)
A_piT_V_L_MainDet = np.array(A_piT_V_L_MainDet)
A_piT_H_L_MainDet = np.array(A_piT_H_L_MainDet)
A_eL_T_MainDet = np.array(A_eL_T_MainDet)
A_eT_V_T_MainDet = np.array(A_eT_V_T_MainDet)
A_eT_H_T_MainDet = np.array(A_eT_H_T_MainDet)
A_piL_T_MainDet = np.array(A_piL_T_MainDet)
A_piT_V_T_MainDet = np.array(A_piT_V_T_MainDet)
A_piT_H_T_MainDet = np.array(A_piT_H_T_MainDet)
print("np.shape(A_eT_V_L_PionDet):", np.shape(A_eT_V_L_PionDet))
print("np.shape(A_eT_H_T_PionDet):", np.shape(A_eT_H_T_PionDet))
print("np.shape(A_piT_V_L_PionDet):", np.shape(A_piT_V_L_PionDet))
print("np.shape(A_piT_H_T_PionDet):", np.shape(A_piT_H_T_PionDet))
print("np.shape(A_eT_V_L_MainDet):", np.shape(A_eT_V_L_MainDet))
print("np.shape(A_eT_H_T_MainDet):", np.shape(A_eT_H_T_MainDet))
print("np.shape(A_piT_V_L_MainDet):", np.shape(A_piT_V_L_MainDet))
print("np.shape(A_piT_H_T_MainDet):", np.shape(A_piT_H_T_MainDet))
#**************************************************************************************************************************************************
theta_L_PionDet = np.zeros((num_PionDet, N_L))
dtheta_L_PionDet = np.zeros((num_PionDet, N_L))
theta_L_MainDet = np.zeros((num_MainDet, N_L))
dtheta_L_MainDet = np.zeros((num_MainDet, N_L))
phi_L_PionDet = np.zeros((num_PionDet, N_L))
dphi_L_PionDet = np.zeros((num_PionDet, N_L))
phi_L_MainDet = np.zeros((num_MainDet, N_L))
dphi_L_MainDet = np.zeros((num_MainDet, N_L))
for iteration in range(N_L):
theta_L_PionDet_i = np.array([theta_L] * num_PionDet)
dtheta_L_PionDet_i = np.array([Theta_uncertainty] * num_PionDet)
theta_L_MainDet_i = np.array([theta_L] * num_MainDet)
dtheta_L_MainDet_i = np.array([Theta_uncertainty] * num_MainDet)
phi_L_PionDet_i = np.array([phi_L] * num_PionDet)
dphi_L_PionDet_i = np.array([Phi_uncertainty] * num_PionDet)
phi_L_MainDet_i = np.array([phi_L] * num_MainDet)
dphi_L_MainDet_i = np.array([Phi_uncertainty] * num_MainDet)
for i in range(num_PionDet):
theta_L_PionDet[i, iteration] = theta_L_PionDet_i[i]
phi_L_PionDet[i, iteration] = phi_L_PionDet_i[i]
for i in range(num_MainDet):
theta_L_MainDet[i, iteration] = theta_L_MainDet_i[i]
phi_L_MainDet[i, iteration] = phi_L_MainDet_i[i]
print("phi_L_PionDet.shape:", phi_L_PionDet.shape)
print("theta_L_PionDet.shape:", theta_L_PionDet.shape)
print("phi_L_MainDet.shape:", phi_L_MainDet.shape)
print("theta_L_MainDet.shape:", theta_L_MainDet.shape)
#**************************************************************************************************************************************************
theta_T_PionDet = np.zeros((num_PionDet, N_T))
dtheta_T_PionDet = np.zeros((num_PionDet, N_T))
theta_T_MainDet = np.zeros((num_MainDet, N_T))
dtheta_T_MainDet = np.zeros((num_MainDet, N_T))
phi_T_PionDet = np.zeros((num_PionDet, N_T))
dphi_T_PionDet = np.zeros((num_PionDet, N_T))
phi_T_MainDet = np.zeros((num_MainDet, N_T))
dphi_T_MainDet = np.zeros((num_MainDet, N_T))
for iteration in range(N_T):
theta_T_PionDet_i = np.array([theta_T] * num_PionDet)
dtheta_T_PionDet_i = np.array([Theta_uncertainty] * num_PionDet)
theta_T_MainDet_i = np.array([theta_T] * num_MainDet)
dtheta_T_MainDet_i = np.array([Theta_uncertainty] * num_MainDet)
phi_T_PionDet_i = np.array([phi_T] * num_PionDet)
dphi_T_PionDet_i = np.array([Phi_uncertainty] * num_PionDet)
phi_T_MainDet_i = np.array([phi_T] * num_MainDet)
dphi_T_MainDet_i = np.array([Phi_uncertainty] * num_MainDet)
for i in range(num_PionDet):
theta_T_PionDet[i, iteration] = theta_T_PionDet_i[i]
phi_T_PionDet[i, iteration] = phi_T_PionDet_i[i]
for i in range(num_MainDet):
theta_T_MainDet[i, iteration] = theta_T_MainDet_i[i]
phi_T_MainDet[i, iteration] = phi_T_MainDet_i[i]
print("phi_T_PionDet.shape:", phi_T_PionDet.shape)
print("theta_T_PionDet.shape:", theta_T_PionDet.shape)
print("phi_T_MainDet.shape:", phi_T_MainDet.shape)
print("theta_T_MainDet.shape:", theta_T_MainDet.shape)
#**************************************************************************************************************************************************
asymmetry_code = """
data {
int<lower=0> num_PionDet;
int<lower=0> num_MainDet;
int<lower=0> N_L;
int<lower=0> N_T;
matrix[num_PionDet, N_L] f_Pi_PionDet_L;
matrix[num_MainDet, N_L] f_Pi_MainDet_L;
matrix[num_PionDet, N_L] A_eL_L_PionDet;
matrix[num_PionDet, N_L] A_eT_V_L_PionDet;
matrix[num_PionDet, N_L] A_eT_H_L_PionDet;
matrix[num_PionDet, N_L] A_piL_L_PionDet;
matrix[num_PionDet, N_L] A_piT_V_L_PionDet;
matrix[num_PionDet, N_L] A_piT_H_L_PionDet;
matrix[num_MainDet, N_L] A_eL_L_MainDet;
matrix[num_MainDet, N_L] A_eT_V_L_MainDet;
matrix[num_MainDet, N_L] A_eT_H_L_MainDet;
matrix[num_MainDet, N_L] A_piL_L_MainDet;
matrix[num_MainDet, N_L] A_piT_V_L_MainDet;
matrix[num_MainDet, N_L] A_piT_H_L_MainDet;
matrix[num_PionDet, N_L] Measured_Asymmetry_PionDet_L;
matrix[num_PionDet, N_L] dMeasured_Asymmetry_PionDet_L;
matrix[num_MainDet, N_L] Measured_Asymmetry_MainDet_L;
matrix[num_MainDet, N_L] dMeasured_Asymmetry_MainDet_L;
matrix[num_PionDet, N_L] theta_L_PionDet;
matrix[num_PionDet, N_L] phi_L_PionDet;
matrix[num_MainDet, N_L] theta_L_MainDet;
matrix[num_MainDet, N_L] phi_L_MainDet;
matrix[num_PionDet, N_T] f_Pi_PionDet_T;
matrix[num_MainDet, N_T] f_Pi_MainDet_T;
matrix[num_PionDet, N_T] A_eL_T_PionDet;
matrix[num_PionDet, N_T] A_eT_V_T_PionDet;
matrix[num_PionDet, N_T] A_eT_H_T_PionDet;
matrix[num_PionDet, N_T] A_piL_T_PionDet;
matrix[num_PionDet, N_T] A_piT_V_T_PionDet;
matrix[num_PionDet, N_T] A_piT_H_T_PionDet;
matrix[num_MainDet, N_T] A_eL_T_MainDet;
matrix[num_MainDet, N_T] A_eT_V_T_MainDet;
matrix[num_MainDet, N_T] A_eT_H_T_MainDet;
matrix[num_MainDet, N_T] A_piL_T_MainDet;
matrix[num_MainDet, N_T] A_piT_V_T_MainDet;
matrix[num_MainDet, N_T] A_piT_H_T_MainDet;
matrix[num_PionDet, N_T] Measured_Asymmetry_PionDet_T;
matrix[num_PionDet, N_T] dMeasured_Asymmetry_PionDet_T;
matrix[num_MainDet, N_T] Measured_Asymmetry_MainDet_T;
matrix[num_MainDet, N_T] dMeasured_Asymmetry_MainDet_T;
matrix[num_PionDet, N_T] theta_T_PionDet;
matrix[num_PionDet, N_T] phi_T_PionDet;
matrix[num_MainDet, N_T] theta_T_MainDet;
matrix[num_MainDet, N_T] phi_T_MainDet;
}
parameters {
real A_eL;
real A_eT;
real A_piL;
real A_piT;
}
model {
//priors
A_eL ~ normal(-33, 1000);
A_eT ~ normal(11000, 100000);
A_piL ~ normal(25400, 100000);
A_piT ~ normal(60100, 100000);
//A_eL ~ normal(-33, 1);
//A_eT ~ normal(11000, 100);
//A_piL ~ normal(25400, 100);
//A_piT ~ normal(60100, 100);
// Model for Pion detector
for (i in 1:num_PionDet)
for (j in 1:N_L)
Measured_Asymmetry_PionDet_L[i, j] ~ normal((1 - f_Pi_PionDet_L[i, j]) * ((A_eL * A_eL_L_PionDet[i,j]) * cos(theta_L_PionDet[i,j]) + A_eT * sin(theta_L_PionDet[i,j]) * (A_eT_V_L_PionDet[i,j]*sin(phi_L_PionDet[i,j])+A_eT_H_L_PionDet[i,j]*cos(phi_L_PionDet[i,j]))) + f_Pi_PionDet_L[i, j] * ((A_piL * A_piL_L_PionDet[i,j]) * cos(theta_L_PionDet[i,j]) + A_piT * sin(theta_L_PionDet[i,j]) * (A_piT_V_L_PionDet[i,j]*sin(phi_L_PionDet[i,j])+A_piT_H_L_PionDet[i,j]*cos(phi_L_PionDet[i,j]))), dMeasured_Asymmetry_PionDet_L[i,j]);
for (i in 1:num_PionDet)
for (j in 1:N_T)
Measured_Asymmetry_PionDet_T[i, j] ~ normal((1 - f_Pi_PionDet_T[i, j]) * ((A_eL * A_eL_T_PionDet[i,j]) * cos(theta_T_PionDet[i,j]) + A_eT * sin(theta_T_PionDet[i,j]) * (A_eT_V_T_PionDet[i,j]*sin(phi_T_PionDet[i,j])+A_eT_H_T_PionDet[i,j]*cos(phi_T_PionDet[i,j]))) + f_Pi_PionDet_T[i, j] * ((A_piL * A_piL_T_PionDet[i,j]) * cos(theta_T_PionDet[i,j]) + A_piT * sin(theta_T_PionDet[i,j]) * (A_piT_V_T_PionDet[i,j]*sin(phi_T_PionDet[i,j])+A_piT_H_T_PionDet[i,j]*cos(phi_T_PionDet[i,j]))), dMeasured_Asymmetry_PionDet_T[i,j]);
// Model for Main detetcor
for (i in 1:num_MainDet)
for (j in 1:N_L)
Measured_Asymmetry_MainDet_L[i, j] ~ normal((1 - f_Pi_MainDet_L[i, j]) * ((A_eL * A_eL_L_MainDet[i,j]) * cos(theta_L_MainDet[i,j]) + A_eT * sin(theta_L_MainDet[i,j]) * (A_eT_V_L_MainDet[i,j]*sin(phi_L_MainDet[i,j])+A_eT_H_L_MainDet[i,j]*cos(phi_L_MainDet[i,j]))) + f_Pi_MainDet_L[i, j] * ((A_piL * A_piL_L_MainDet[i,j]) * cos(theta_L_MainDet[i,j]) + A_piT * sin(theta_L_MainDet[i,j]) * (A_piT_V_L_MainDet[i,j]*sin(phi_L_MainDet[i,j])+A_piT_H_L_MainDet[i,j]*cos(phi_L_MainDet[i,j]))), dMeasured_Asymmetry_MainDet_L[i,j]);
for (i in 1:num_MainDet)
for (j in 1:N_T)
Measured_Asymmetry_MainDet_T[i, j] ~ normal((1 - f_Pi_MainDet_T[i, j]) * ((A_eL * A_eL_T_MainDet[i,j]) * cos(theta_T_MainDet[i,j]) + A_eT * sin(theta_T_MainDet[i,j]) * (A_eT_V_T_MainDet[i,j]*sin(phi_T_MainDet[i,j])+A_eT_H_T_MainDet[i,j]*cos(phi_T_MainDet[i,j]))) + f_Pi_MainDet_T[i, j] * ((A_piL * A_piL_T_MainDet[i,j]) * cos(theta_T_MainDet[i,j]) + A_piT * sin(theta_T_MainDet[i,j]) * (A_piT_V_T_MainDet[i,j]*sin(phi_T_MainDet[i,j])+A_piT_H_T_MainDet[i,j]*cos(phi_T_MainDet[i,j]))), dMeasured_Asymmetry_MainDet_T[i,j]);
}
"""
#**************************************************************************************************************************************************
#Put our data in a dictionary
asym_data = {
'num_PionDet': num_PionDet,
'num_MainDet': num_MainDet,
'N_L': N_L,
'N_T': N_T,
'f_Pi_PionDet_L':f_Pi_PionDet_L,
'f_Pi_MainDet_L':f_Pi_MainDet_L,
'f_Pi_PionDet_T':f_Pi_PionDet_T,
'f_Pi_MainDet_T':f_Pi_MainDet_T,
'Measured_Asymmetry_PionDet_L': Measured_Asymmetry_PionDet_L,
'dMeasured_Asymmetry_PionDet_L': dMeasured_Asymmetry_PionDet_L,
'Measured_Asymmetry_MainDet_L': Measured_Asymmetry_MainDet_L,
'dMeasured_Asymmetry_MainDet_L': dMeasured_Asymmetry_MainDet_L,
'Measured_Asymmetry_PionDet_T': Measured_Asymmetry_PionDet_T,
'dMeasured_Asymmetry_PionDet_T': dMeasured_Asymmetry_PionDet_T,
'Measured_Asymmetry_MainDet_T': Measured_Asymmetry_MainDet_T,
'dMeasured_Asymmetry_MainDet_T': dMeasured_Asymmetry_MainDet_T,
'A_eL_L_PionDet': A_eL_L_PionDet,
'A_eT_V_L_PionDet': A_eT_V_L_PionDet,
'A_eT_H_L_PionDet': A_eT_H_L_PionDet,
'A_piL_L_PionDet': A_piL_L_PionDet,
'A_piT_V_L_PionDet': A_piT_V_L_PionDet,
'A_piT_H_L_PionDet': A_piT_H_L_PionDet,
'A_eL_L_MainDet': A_eL_L_MainDet,
'A_eT_V_L_MainDet': A_eT_V_L_MainDet,
'A_eT_H_L_MainDet': A_eT_H_L_MainDet,
'A_piL_L_MainDet': A_piL_L_MainDet,
'A_piT_V_L_MainDet': A_piT_V_L_MainDet,
'A_piT_H_L_MainDet': A_piT_H_L_MainDet,
'A_eL_T_PionDet': A_eL_T_PionDet,
'A_eT_V_T_PionDet': A_eT_V_T_PionDet,
'A_eT_H_T_PionDet': A_eT_H_T_PionDet,
'A_piL_T_PionDet': A_piL_T_PionDet,
'A_piT_V_T_PionDet': A_piT_V_T_PionDet,
'A_piT_H_T_PionDet': A_piT_H_T_PionDet,
'A_eL_T_MainDet': A_eL_T_MainDet,
'A_eT_V_T_MainDet': A_eT_V_T_MainDet,
'A_eT_H_T_MainDet': A_eT_H_T_MainDet,
'A_piL_T_MainDet': A_piL_T_MainDet,
'A_piT_V_T_MainDet': A_piT_V_T_MainDet,
'A_piT_H_T_MainDet': A_piT_H_T_MainDet,
'theta_L_PionDet': theta_L_PionDet,
'phi_L_PionDet': phi_L_PionDet,
'theta_L_MainDet': theta_L_MainDet,
'phi_L_MainDet': phi_L_MainDet,
'theta_T_PionDet': theta_T_PionDet,
'phi_T_PionDet': phi_T_PionDet,
'theta_T_MainDet': theta_T_MainDet,
'phi_T_MainDet': phi_T_MainDet,
}
#print("asym_data=", asym_data)
print("N_L:", N_L)
print("N_T:", N_T)
#**************************************************************************************************************************************************
# Compile the model and generate samples
model = pystan.StanModel(model_code=asymmetry_code)
# Train the model and generate samples
asym_fit = model.sampling(data=asym_data, seed=321, iter=10500, chains=1, warmup=500)
# Get summary of the fit
summary = asym_fit.summary()
# Convert the summary to a DataFrame if you prefer it in that format
summary_df = pd.DataFrame(summary['summary'], columns=summary['summary_colnames'], index=summary['summary_rownames'])
#print(summary)
print("summary_df:\n", summary_df)
# Extracting the sampled data into a dictionary
fit_data = asym_fit.extract(permuted=True)
# Converting the dictionary into a DataFrame
# For a simple example, let's assume we're only interested in some specific parameters
# If you have multidimensional parameters, you'll need to handle them appropriately
fit_df = pd.DataFrame({
'A_eL': fit_data['A_eL'],
'A_eT': fit_data['A_eT'],
'A_piL': fit_data['A_piL'],
'A_piT': fit_data['A_piT']
})
# Saving the DataFrame to a CSV file
fit_df.to_csv('asymmetry_parameters.csv', index=False)
#**************************************************************************************************************************************************
# Accessing parameter estimates and their standard deviations from the summary DataFrame
A_eL = summary_df.loc['A_eL', 'mean']
A_eT = summary_df.loc['A_eT', 'mean']
A_piL = summary_df.loc['A_piL', 'mean']
A_piT = summary_df.loc['A_piT', 'mean']
print(f"A_eL: {A_eL}, A_eT: {A_eT}, A_piL: {A_piL}, A_piT: {A_piT}")
dA_eL = summary_df.loc['A_eL', 'sd']
dA_eT = summary_df.loc['A_eT', 'sd']
dA_piL = summary_df.loc['A_piL', 'sd']
dA_piT = summary_df.loc['A_piT', 'sd']
print(f"dA_eL: {dA_eL}, dA_eT: {dA_eT}, dA_piL: {dA_piL}, dA_piT: {dA_piT}")
#**************************************************************************************************************************************************
#Calculate the correlation matrix and covariance matrix:
# Extract parameter samples from the fit
samples = asym_fit.extract(permuted=True)
# Creating the DataFrame from samples
df = pd.DataFrame({
"A_eL": samples['A_eL'],
"A_eT": samples['A_eT'],
"A_piL": samples['A_piL'],
"A_piT": samples['A_piT'],
})
# Calculate the correlation matrix and covariance matrix
correlation_matrix = df.corr()
covariance_matrix = df.cov()
print("correlation_matrix = ", correlation_matrix)
print("covariance_matrix = ", covariance_matrix)
#**************************************************************************************************************************************************
#Plot the Covariance matrix:
# Enable LaTeX rendering in matplotlib
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
# Define the mapping of names to formatted LaTeX names
name_map = {
'A_eL': r'$A_e^L$',
'A_eT': r'$A_e^T$',
'A_piL': r'$A_{\pi}^L$',
'A_piT': r'$A_{\pi}^T$'
}
# Create a 4x4 subplot grid
fig, axes = plt.subplots(4, 4, figsize=(12, 12))
variables = list(name_map.keys())
# Generate each plot in the grid
for i in range(4):
for j in range(4):
if i != j:
sns.kdeplot(data=df, x=variables[j], y=variables[i], ax=axes[i, j], cmap='viridis', fill=True, levels=10)
else:
# Plot the distribution of the variable in the diagonal
sns.histplot(data=df, x=variables[j], ax=axes[i, j], color='blue', kde=True)
# Set LaTeX formatted labels
axes[i, j].set_xlabel(name_map[variables[j]])
axes[i, j].set_ylabel(name_map[variables[i]])
# Adjust layout to prevent overlap
plt.tight_layout()
plt.savefig('Covariance.png')
#**************************************************************************************************************************************************
#Plot the Partial Covariance matrix:
# List of pairs to plot
pairs = [
('A_eL', 'A_eT'),
('A_eL', 'A_piL'),
('A_eL', 'A_piT'),
('A_eT', 'A_piL'),
('A_eT', 'A_piT'),
('A_piL', 'A_piT')
]
# Create a 2x3 subplot grid
fig, axes = plt.subplots(2, 3, figsize=(10, 6))
axes = axes.flatten() # Flatten the array of axes to make indexing easier
# Generate each plot in the specified positions
for i, (x, y) in enumerate(pairs):
sns.kdeplot(data=df, x=x, y=y, ax=axes[i], cmap='viridis', fill=False, levels=10) # Consider using fill=True for better visual
# Update axis labels using the name map for better readability
axes[i].set_xlabel(name_map[x])
axes[i].set_ylabel(name_map[y])
axes[i].grid(False)
# Adjust the layout to prevent label overlap and ensure everything fits well
plt.tight_layout()
plt.savefig('PartialCovariance.png')
#**************************************************************************************************************************************************
#Calculate fitted asymmetry uncertainties (pion detectors) and propagation of uncertainty with respect to the exteracted parameters, A_eL, A_eT, A_piL, A_piT:
Measured_Asymmetry_PionDet_L_Fitted = np.zeros((num_PionDet, N_L))
partial_A_eL_PionDet_L = np.zeros((num_PionDet, N_L))
partial_A_eT_PionDet_L = np.zeros((num_PionDet, N_L))
partial_A_piL_PionDet_L = np.zeros((num_PionDet, N_L))
partial_A_piT_PionDet_L = np.zeros((num_PionDet, N_L))
dMeasured_Asymmetry_PionDet_L_Fitted = np.zeros((num_PionDet, N_L))
Measured_Asymmetry_PionDet_T_Fitted = np.zeros((num_PionDet, N_T))
partial_A_eL_PionDet_T = np.zeros((num_PionDet, N_T))
partial_A_eT_PionDet_T = np.zeros((num_PionDet, N_T))
partial_A_piL_PionDet_T = np.zeros((num_PionDet, N_T))
partial_A_piT_PionDet_T = np.zeros((num_PionDet, N_T))
dMeasured_Asymmetry_PionDet_T_Fitted = np.zeros((num_PionDet, N_T))
# Model for Pion detector
for i in range(num_PionDet):
for j in range(N_L):
Measured_Asymmetry_PionDet_L_Fitted[i,j] = (1 - f_Pi_PionDet_L[i,j]) * (A_eL * A_eL_L_PionDet[i,j] * np.cos(theta_L_PionDet[i, j]) + A_eT * np.sin(theta_L_PionDet[i, j]) * (A_eT_V_L_PionDet[i, j] * np.sin(phi_L_PionDet[i, j]) + A_eT_H_L_PionDet[i, j] * np.cos(phi_L_PionDet[i, j]))) + f_Pi_PionDet_L[i, j] * ((A_piL * A_piL_L_PionDet[i,j]) * np.cos(theta_L_PionDet[i, j]) + A_piT * np.sin(theta_L_PionDet[i, j]) * (A_piT_V_L_PionDet[i, j] * np.sin(phi_L_PionDet[i, j]) + A_piT_H_L_PionDet[i, j] * np.cos(phi_L_PionDet[i, j])))
partial_A_eL_PionDet_L[i, j] = (1 - f_Pi_PionDet_L[i, j]) * A_eL_L_PionDet[i, j] * np.cos(theta_L_PionDet[i, j])
partial_A_eT_PionDet_L[i, j] = (1 - f_Pi_PionDet_L[i, j]) * np.sin(theta_L_PionDet[i, j]) * (A_eT_V_L_PionDet[i, j] * np.sin(phi_L_PionDet[i, j]) + A_eT_H_L_PionDet[i, j] * np.cos(phi_L_PionDet[i, j]))
partial_A_piL_PionDet_L[i, j] = f_Pi_PionDet_L[i, j] * A_piL_L_PionDet[i, j] * np.cos(theta_L_PionDet[i, j])
partial_A_piT_PionDet_L[i, j] = f_Pi_PionDet_L[i, j] * np.sin(theta_L_PionDet[i, j]) * (A_piT_V_L_PionDet[i, j] * np.sin(phi_L_PionDet[i, j]) + A_piT_H_L_PionDet[i, j] * np.cos(phi_L_PionDet[i, j]))
# Propagate the uncertainties
dMeasured_Asymmetry_PionDet_L_Fitted[i, j] = np.sqrt(
(partial_A_eL_PionDet_L[i, j] * dA_eL) ** 2 +
(partial_A_eT_PionDet_L[i, j] * dA_eT) ** 2 +
(partial_A_piL_PionDet_L[i, j] * dA_piL) ** 2 +
(partial_A_piT_PionDet_L[i, j] * dA_piT) ** 2
)
for i in range(num_PionDet):
for j in range(N_T):
Measured_Asymmetry_PionDet_T_Fitted[i,j] = (1 - f_Pi_PionDet_T[i,j]) * (A_eL * A_eL_T_PionDet[i,j] * np.cos(theta_T_PionDet[i, j]) + A_eT * np.sin(theta_T_PionDet[i, j]) * (A_eT_V_T_PionDet[i, j] * np.sin(phi_T_PionDet[i, j]) + A_eT_H_T_PionDet[i, j] * np.cos(phi_T_PionDet[i, j]))) + f_Pi_PionDet_T[i, j] * ((A_piL * A_piL_T_PionDet[i,j]) * np.cos(theta_T_PionDet[i, j]) + A_piT * np.sin(theta_T_PionDet[i, j]) * (A_piT_V_T_PionDet[i, j] * np.sin(phi_T_PionDet[i, j]) + A_piT_H_T_PionDet[i, j] * np.cos(phi_T_PionDet[i, j])))
partial_A_eL_PionDet_T[i, j] = (1 - f_Pi_PionDet_T[i, j]) * A_eL_T_PionDet[i, j] * np.cos(theta_T_PionDet[i, j])
partial_A_eT_PionDet_T[i, j] = (1 - f_Pi_PionDet_T[i, j]) * np.sin(theta_T_PionDet[i, j]) * (A_eT_V_T_PionDet[i, j] * np.sin(phi_T_PionDet[i, j]) + A_eT_H_T_PionDet[i, j] * np.cos(phi_T_PionDet[i, j]))
partial_A_piL_PionDet_T[i, j] = f_Pi_PionDet_T[i, j] * A_piL_T_PionDet[i, j] * np.cos(theta_T_PionDet[i, j])
partial_A_piT_PionDet_T[i, j] = f_Pi_PionDet_T[i, j] * np.sin(theta_T_PionDet[i, j]) * (A_piT_V_T_PionDet[i, j] * np.sin(phi_T_PionDet[i, j]) + A_piT_H_T_PionDet[i, j] * np.cos(phi_T_PionDet[i, j]))
# Propagate the uncertainties
dMeasured_Asymmetry_PionDet_T_Fitted[i, j] = np.sqrt(
(partial_A_eL_PionDet_T[i, j] * dA_eL) ** 2 +
(partial_A_eT_PionDet_T[i, j] * dA_eT) ** 2 +
(partial_A_piL_PionDet_T[i, j] * dA_piL) ** 2 +
(partial_A_piT_PionDet_T[i, j] * dA_piT) ** 2
)
#**************************************************************************************************************************************************
#Calculate fitted asymmetry uncertainties (main detector) and propagation of uncertainty with respect to the exteracted parameters, A_eL, A_eT, A_piL, A_piT:
Measured_Asymmetry_MainDet_L_Fitted = np.zeros((num_MainDet, N_L))
partial_A_eL_MainDet_L = np.zeros((num_MainDet, N_L))
partial_A_eT_MainDet_L = np.zeros((num_MainDet, N_L))
partial_A_piL_MainDet_L = np.zeros((num_MainDet, N_L))
partial_A_piT_MainDet_L = np.zeros((num_MainDet, N_L))
dMeasured_Asymmetry_MainDet_L_Fitted = np.zeros((num_MainDet, N_L))
Measured_Asymmetry_MainDet_T_Fitted = np.zeros((num_MainDet, N_T))
partial_A_eL_MainDet_T = np.zeros((num_MainDet, N_T))
partial_A_eT_MainDet_T = np.zeros((num_MainDet, N_T))
partial_A_piL_MainDet_T = np.zeros((num_MainDet, N_T))
partial_A_piT_MainDet_T = np.zeros((num_MainDet, N_T))
dMeasured_Asymmetry_MainDet_T_Fitted = np.zeros((num_MainDet, N_T))
# Model for Main detector
for i in range(num_MainDet):
for j in range(N_L):
Measured_Asymmetry_MainDet_L_Fitted[i,j] = (1 - f_Pi_MainDet_L[i,j]) * (A_eL * A_eL_L_MainDet[i,j] * np.cos(theta_L_MainDet[i, j]) + A_eT * np.sin(theta_L_MainDet[i, j]) * (A_eT_V_L_MainDet[i, j] * np.sin(phi_L_MainDet[i, j]) + A_eT_H_L_MainDet[i, j] * np.cos(phi_L_MainDet[i, j]))) + f_Pi_MainDet_L[i, j] * ((A_piL * A_piL_L_MainDet[i,j]) * np.cos(theta_L_MainDet[i, j]) + A_piT * np.sin(theta_L_MainDet[i, j]) * (A_piT_V_L_MainDet[i, j] * np.sin(phi_L_MainDet[i, j]) + A_piT_H_L_MainDet[i, j] * np.cos(phi_L_MainDet[i, j])))
partial_A_eL_MainDet_L[i, j] = (1 - f_Pi_MainDet_L[i, j]) * A_eL_L_MainDet[i, j] * np.cos(theta_L_MainDet[i, j])
partial_A_eT_MainDet_L[i, j] = (1 - f_Pi_MainDet_L[i, j]) * np.sin(theta_L_MainDet[i, j]) * (A_eT_V_L_MainDet[i, j] * np.sin(phi_L_MainDet[i, j]) + A_eT_H_L_MainDet[i, j] * np.cos(phi_L_MainDet[i, j]))
partial_A_piL_MainDet_L[i, j] = f_Pi_MainDet_L[i, j] * A_piL_L_MainDet[i, j] * np.cos(theta_L_MainDet[i, j])
partial_A_piT_MainDet_L[i, j] = f_Pi_MainDet_L[i, j] * np.sin(theta_L_MainDet[i, j]) * (A_piT_V_L_MainDet[i, j] * np.sin(phi_L_MainDet[i, j]) + A_piT_H_L_MainDet[i, j] * np.cos(phi_L_MainDet[i, j]))
# Propagate the uncertainties
dMeasured_Asymmetry_MainDet_L_Fitted[i, j] = np.sqrt(
(partial_A_eL_MainDet_L[i, j] * dA_eL) ** 2 +
(partial_A_eT_MainDet_L[i, j] * dA_eT) ** 2 +
(partial_A_piL_MainDet_L[i, j] * dA_piL) ** 2 +
(partial_A_piT_MainDet_L[i, j] * dA_piT) ** 2
)
for i in range(num_MainDet):
for j in range(N_T):
Measured_Asymmetry_MainDet_T_Fitted[i,j] = (1 - f_Pi_MainDet_T[i,j]) * (A_eL * A_eL_T_MainDet[i,j] * np.cos(theta_T_MainDet[i, j]) + A_eT * np.sin(theta_T_MainDet[i, j]) * (A_eT_V_T_MainDet[i, j] * np.sin(phi_T_MainDet[i, j]) + A_eT_H_T_MainDet[i, j] * np.cos(phi_T_MainDet[i, j]))) + f_Pi_MainDet_T[i, j] * ((A_piL * A_piL_T_MainDet[i,j]) * np.cos(theta_T_MainDet[i, j]) + A_piT * np.sin(theta_T_MainDet[i, j]) * (A_piT_V_T_MainDet[i, j] * np.sin(phi_T_MainDet[i, j]) + A_piT_H_T_MainDet[i, j] * np.cos(phi_T_MainDet[i, j])))
partial_A_eL_MainDet_T[i, j] = (1 - f_Pi_MainDet_T[i, j]) * A_eL_T_MainDet[i, j] * np.cos(theta_T_MainDet[i, j])
partial_A_eT_MainDet_T[i, j] = (1 - f_Pi_MainDet_T[i, j]) * np.sin(theta_T_MainDet[i, j]) * (A_eT_V_T_MainDet[i, j] * np.sin(phi_T_MainDet[i, j]) + A_eT_H_T_MainDet[i, j] * np.cos(phi_T_MainDet[i, j]))
partial_A_piL_MainDet_T[i, j] = f_Pi_MainDet_T[i, j] * A_piL_T_MainDet[i, j] * np.cos(theta_T_MainDet[i, j])
partial_A_piT_MainDet_T[i, j] = f_Pi_MainDet_T[i, j] * np.sin(theta_T_MainDet[i, j]) * (A_piT_V_T_MainDet[i, j] * np.sin(phi_T_MainDet[i, j]) + A_piT_H_T_MainDet[i, j] * np.cos(phi_T_MainDet[i, j]))
# Propagate the uncertainties
dMeasured_Asymmetry_MainDet_T_Fitted[i, j] = np.sqrt(
(partial_A_eL_MainDet_T[i, j] * dA_eL) ** 2 +
(partial_A_eT_MainDet_T[i, j] * dA_eT) ** 2 +
(partial_A_piL_MainDet_T[i, j] * dA_piL) ** 2 +
(partial_A_piT_MainDet_T[i, j] * dA_piT) ** 2
)
#**************************************************************************************************************************************************
#Save asymmetry values and their uncertainties for the analysis:
Measured_Asymmetry_PionDet_L_Fitted_mean = np.mean(Measured_Asymmetry_PionDet_L_Fitted, axis=1)
df_PionDet_L_Fitted = pd.DataFrame(Measured_Asymmetry_PionDet_L_Fitted_mean, columns=['Asymmetry_PionDet_L_Fitted_mean'])
df_PionDet_L_Fitted.to_csv('Asymmetry_PionDet_L_Fitted_mean.csv', index=False)
#dA_Measured_Asymmetry_PionDet_L_Fitted_mean = np.std(Measured_Asymmetry_PionDet_L_Fitted, axis=1)
dA_Measured_Asymmetry_PionDet_L_Fitted_mean = np.mean(dMeasured_Asymmetry_PionDet_L_Fitted, axis=1)
df_PionDet_L_Fitted_Uncertainty = pd.DataFrame(dA_Measured_Asymmetry_PionDet_L_Fitted_mean, columns=['dAsymmetry_PionDet_L_Fitted_mean'])
df_PionDet_L_Fitted_Uncertainty.to_csv('dAsymmetry_PionDet_L_Fitted_mean.csv', index=False)
Measured_Asymmetry_MainDet_L_Fitted_mean = np.mean(Measured_Asymmetry_MainDet_L_Fitted, axis=1)
df_MainDet_L_Fitted = pd.DataFrame(Measured_Asymmetry_MainDet_L_Fitted_mean, columns=['Asymmetry_MainDet_L_Fitted_mean'])
df_MainDet_L_Fitted.to_csv('Asymmetry_MainDet_L_Fitted_mean.csv', index=False)
#dA_Measured_Asymmetry_MainDet_L_Fitted_mean = np.std(Measured_Asymmetry_MainDet_L_Fitted, axis=1)
dA_Measured_Asymmetry_MainDet_L_Fitted_mean = np.mean(dMeasured_Asymmetry_MainDet_L_Fitted, axis=1)
df_MainDet_L_Fitted_Uncertainty = pd.DataFrame(dA_Measured_Asymmetry_MainDet_L_Fitted_mean, columns=['dAsymmetry_MainDet_L_Fitted_mean'])
df_MainDet_L_Fitted_Uncertainty.to_csv('dAsymmetry_MainDet_L_Fitted_mean.csv', index=False)
Measured_Asymmetry_PionDet_T_Fitted_mean = np.mean(Measured_Asymmetry_PionDet_T_Fitted, axis=1)
df_PionDet_T_Fitted = pd.DataFrame(Measured_Asymmetry_PionDet_T_Fitted_mean, columns=['Asymmetry_PionDet_T_Fitted_mean'])
df_PionDet_T_Fitted.to_csv('Asymmetry_PionDet_T_Fitted_mean.csv', index=False)
#dA_Measured_Asymmetry_PionDet_T_Fitted_mean = np.std(Measured_Asymmetry_PionDet_T_Fitted, axis=1)
dA_Measured_Asymmetry_PionDet_T_Fitted_mean = np.mean(dMeasured_Asymmetry_PionDet_T_Fitted, axis=1)
df_PionDet_T_Fitted_Uncertainty = pd.DataFrame(dA_Measured_Asymmetry_PionDet_T_Fitted_mean, columns=['dAsymmetry_PionDet_T_Fitted_mean'])
df_PionDet_T_Fitted_Uncertainty.to_csv('dAsymmetry_PionDet_T_Fitted_mean.csv', index=False)